IB Math Studies Functions
Questions and Answers
1. IB Mathematical Studies SL – Functions, simplest form
How can I find in simplest form ,where
.
Solution
IB Mathematical Studies SL – Functions, simplest form
The functions in simplest form are:
2. IB Mathematical Studies SL – Linear Functions
How can we find a formula that describes the cost of running a car if there is a standard cost of $100 plus $0.1 per one kilometer thereafter?
Solution
IB Mathematical Studies SL – Linear Functions
Let x be the kilometers then the linear function that describes the above word problem is:
3. IB Mathematical Studies SL – Quadratic Functions
The profit of a PC manufacturer company of making x personal computers (PC) per day is given by the following formula:
How can we find the profit in dollars in the following cases:
for 10 PCs, 40PCs and 100PCs
Solution
IB Mathematical Studies SL – Quadratic Functions
The profit of the company when being produced 10 PCs is given by
The profit of the company when being produced 40 PCs is given
The profit of the company when it produces 100 PCs is given
4. IB Mathematical Studies SL – Complete the square
How can we complete the square and find the vertex of the following quadratic function:
Solution
IB Mathematical Studies SL – Complete the square
Completing the square is a procedure for reformatting quadratic functions.
Quadratic Functions of the form can be rewritten as
The major reason for doing this is that it allows us to easily see the vertex of the curve which is located at the point
.
The general method of completing the square can be shown like this:
Therefore the x-coordinate of the vertex is
Concerning this question if we follow the preceding procedure we have:
Therefore the coordinates of the vertex are
5. IB Mathematical Studies SL – Factorisation
How can we factorize this expression ?
Solution
IB Mathematical Studies SL – Factorization, difference of squares
We‘ll use the difference of squares identity
Concerning this question the factorization is
6. IB Mathematical Studies SL – Factorisation, Common Factor
How can we fully factorize the following expression:
?
Solution
IB Mathematical Studies SL – Factorisation, common factor
The expression can be factorized as follows
?